# [Mental Math] Square Root of [X]

**Question**:

What is the square root of 100,000?; or What is the square root of 7,000,000?

**Answer**:

The interviewer is obviously not looking to get an exact answer to the decimal point but rather is looking to see how you approach the math in your head.

Starting with the second question (square root of 7,000,000) – because you know 1,000 x 1,000 is 1,000,000 and square root of 7 is between 2 and 3, you know it will fall somewhere between 2,000 and 3,000. In order to edge closer, do 25 x 25 which gets you 625 and 27 x 27 which gets you 729. You know the answer is approximately 2,600 (exact answer is 2,645.75). This is simply a process of narrowing down to get to a point where you can approximate the answer.

For the first question (square root of 100,000), 100 x 100 is 10,000 and 1,000 x 1,000 is 1,000,000. Here you want to apply the distributive property from algebra and make this into 10(100×100) = 100,000. Now, you know that square root of 10 falls somewhere between 3 and 4 but much closer to 3. To narrow it down, do 31 x 31 = 961 and 32 x 32 = 1,024. You know the answer is approximately 315 (exact answer is 316.23).

Again, the question is intended to test mental math but also how you approach the question. Walk the interviewer through your math and approach as you solve them, especially for question 1 where it’s not just a process of narrowing down your answer but an extra step of deconstructing the number to a point where you can start mental math.

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